Brief introduction to Thermodynamics

Understanding Heat and Temperature.

Zeroth Law of Thermodynamics and Thermal Equilibrium. How do Thermometers work ?

3 important temperature scales are Kelvin, Celsius and Fahrenheit.

At what temperature do the Celsius and Fahrenheit readings have the same numerical value?

Introduces coefficient of Linear expansion and Thermal Strain.

A steel wire of 1 mm2 cross section is held straight (but under no tension) by attaching it firmly to two points a distance 1 m apart at 40 oC. If the temperature now decreases to -40 oC, and if the two tie points remain fixed, what will be the tension in the wire ? For steel, Y = 200000 MPa.

A= 1.2 x 10-5 oC -1

Two rods of different materials having coefficients of thermal expansion a1 and a2 and Youngs modulus Y1 and Y2 are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

It is desired to put an iron rim on a wooden wheel. The diameter of the wheel is

1 m and the inside diameter of the rim is 0.98 m. If the rim is at 20 oC initially, to what temperature must it be heated to just fit onto the wheel?

Functioning and Uses of a Bimetallic Strip

A bimetallic strip is formed out of two identical strips of two different metals. The co-efficient of linear expansion of the two metals are a1 and a2. When the temperature of the strip is increased by DT, it bends to form an arc of radius of curvature R. Then R is

a) Proportional to DT

b) inversely proportional to DT

c) Proportional to ( a1 - a2 )

d) inversely proportional to ( a1 - a2 )

Superficial and Volume expansion on Heating. Actual and Apparent Volume expansion of Fluids.

A sheet of copper has an area of 1000 cm2 at -50 oC. Find the area of this sheet at 100 oC.

What is the increase in Surface area of a ball, when its temperature is increased by DT. Given, the coefficient of linear expansion of material is a a

Why does water expand on cooling below 4 degree centigrade ? Or why does Ice float on water ?

Density of water is maximum at

a) 0 oC

b) 2 oC

c) 4 oC

d) 6 oC

Heat Capacity, Specific Heat Capacity and Molar Heat Capacity.

In an experiment is it observed that it takes 3360 J of heat to change the temperature of 2 kg glass by 2 oC and it takes 4 k cal of heat to change the temperature of 1 kg Water by 4 oC. Compare the specific heat capacities of glass and water.

Does Heat supply always increase the Temperature of body ? How is it possible to have Water and Ice at 0 degree ?

1 kg Ice at -100 oC is converted into Steam at 100 oC.

Calculate the heat required in each of the following steps.

a) ice at -100 oC is brought to ice at 0 oC

b) ice at 0 oC is converted into water at 0 oC

c) water at 0 oC is brought to water at 100 oC

d) water at 100 oC is converted into steam at 100 oC

Given:

Specific heat capacity of ice = 0.5 k cal / kg oC

Specific heat capacity of water = 1 k cal / kg oC

Latent heat of Fusion of ice = 80 k cal / kg oC

Latent heat of Vaporization of water = 540 k cal / kg oC

A block of ice at -10 oC is slowly heated and converted to steam at 100 oC. Which of the flowing curves represents the phenomenon qualitatively?

In a closed and isolate environment, Total Heat lost by one body will be equal to the total heat gained by another body.

2 kg of ice at -20 oC is mixed with 5 kg of water at 20 oC in an insulating vessel having a negligible heat capacity. Calculate the final mass of water in the vessel. It is given that the specific heat of water and ice are 1 k cal / kg / oC and 0.5 k cal / kg / oC respectively and the latent heat of fusion of ice is 80 k cal / kg.

a) 7 kg

b) 6 kg

c) 4 kg

d) 2 kg

300 g of water at 25 oC is added to 100 g of ice at 0 oC. The final temperature of the mixture is

Steam at 100 oC is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at 15 oC till the temperature of the calorimeter rises to 80 oC. The mass of steam condensed in kilogram is

a) 0.13

b) 0.065

c) 0.260

d) 0.135

400g of ice at 253 K is mixed with 0.05 kg of steam at 100 oC. Latent heat of vaporization of steam = 540 cal/g. Latent heat of fusion of ice = 80 cal/g. Specific heat of ice 0.5 cal/g oC. The resultant temperature of the mixture is

What should be the lengths of steel and copper rod so that the length of steel rod is 5 cm longer than the copper rod at all temperatures?

Two rods, one made of aluminium and the other made of steel, have initial lengths l1 and l2 respectively. The coefficients of linear expansion for aluminium and steel are a1 and a2 respectively. If the length of each rod increases by the same amount when their temperature is raised by T oC, then the ratio l1 /(l1 + l2)

A composite rod is made by joining a copper rod, end to end, with a second rod of a different material but of the same cross section. At 25 oC, the composite rod is 1m in length of which the length of the copper rod is 30 cm. At 125 oC the length of the composite rod increases by 2 mm. The co-efficient of linear expansion of copper is ac = 1.7 x 10-5 per oC and that of the second rod is ax = n x 10-5 per oC. Find the value of n.

A steel scale measures the length of a copper rod as 80.0 cm when both are at 20 oC, the temperature at which the scale is calibrated. What will be the scale reading for the length of the rod when both are at 40 oC?

A traditional clock has a pendulum made of metal. The clock is adjusted to have a period of 1s exactly at 15 oC. When operated at 40 oC, will it be fast or slow?

How much will the clock be in error 1 month after it is set?

At 20 oC, a pendulum clock shows accurate time at a place where g = 9.800 m/s2. This pendulum is taken to a place where g = 9.788 m/s2?

Find the temperature at which it will give accurate time again.

If an anisotropic solid has coefficients of linear expansion ax, ay, and az for three mutually perpendicular directions in the solid, what is the coefficient of volume expansion for the solid?

A substance of mass M requires power input P to remain in the molten state at its melting point. When the power source is turned off, the sample completely solidifies in time t. The latent heat of fusion of the substance is

a) Pt / M

b) Mt / P

c) P / Mt

d) PMt

A 1 kW electric kettle contains 2 liter water at 27 oC. The kettle is operated for 10 minutes. If heat is lost to the surrounding at a constant rate of 160 J/sec, the temperature attained by water in 10 minutes will be (specific heat of water = 4.2 kJ/ kg oC) a) 57o C b) 67o C c) 77o C d) 87o C

In an industrial process 10 kg of water per hour is to be heated from 20 oC to

80 oC. To do this, steam at 150 oC is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at 90 oC. How many kg of steam is required per hour?

Specific heat of steam = 1 cal / gm oC = 1 kilo cal / kg oC

Latent heat of steam = 540 cal / gm = 540 kilo cal / kg.

20 g of ice in 10 g copper calorimeter is originally at -30 oC. How much steam at 100 oC must be condensed in the calorimeter if the ice is to be changed to water and heated to 40 oC ? Latent heat of vaporization of

water = 540 cal / g.

Latent heat of fusion ice = 80 cal / g.

Specific heat of copper = 0.092 cal / g oC

and specific heat of ice = 0.5 cal / g oC

The temperatures of equal masses of three different liquid A, B and C are 12 oC, 19 oC and 28 oC respectively. The temperature when A and B are mixed is 16 oC and when B and C are mixed, it is 23 oC. What should be the temperature when A and C are mixed?

Ice at 0 oC is added to 200 g of water initially at 70 oC in a vacuum flask. When 50 g of ice has been added and has all melted, the temperature of the flask and contents is 40 oC. When a further 80 g of ice has been added and has all melted, the temperature of the whole becomes 10 oC. Neglecting heat loss to surroundings calculates latent heat of fusion of ice.

An open iron container of volume 500 mL is full of glycerin at 10 oC. What volume of glycerin overflows when the container if heated to 160 oC ?

A one liter flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same.

What is the volume of mercury in flask?

Given:

Coefficient of linear expansion of glass = 9 x 10-6 per degree,

Coefficient of volume expansion of mercury = 1.8 x 10-4 per degree

Let Dl1 be the length of the column in a mercury thermometer which corresponds to a rise in temperature DT if the expansion of the glass is neglected. Let Dl2 be the actual length which allows for the expansion of the glass. Calculate the numerical value of (Dl1 - Dl2) / Dl1.

Only the bulb is immersed in the object whose temperature is being measured

The mercury in a thermometer has volume of 210 mm3 at 0 oC, at which temperature the diameter of the bore is 0.2 mm. How far apart are the degree marks on the stem ?

A vessel is completely filled with 500 gm of water and 1000 gm of mercury. When 21200 calories of heat are given to it, 3.52 gm of water overflows. Calculate the coefficient of volume expansion of mercury. Expansion of vessel may be neglected. Given, Coefficient of volume expansion of water = 1.5 10-4 per degree centigrade Density of mercury = 13.6 gm/cm3 Specific heat of mercury = 0.03 cal/gm oC

When the expansion of a liquid in a vessel is measured to obtain the coefficient g, what is actually obtained is g relative to the material of which the container is made. Figure shows an apparatus from which the correct value of g can be found without any knowledge of g for the container.

Show that:

A sinker of weights Wo has an apparent weight W1 when weighed in a liquid at a temperature T1 and W2 when weighed in the same liquid at a temperature T2. The coefficient of cubical expansion of the material of sinker is g . What is the coefficient of volume expansion of the liquid?

A metal ball immersed in alcohol weighs W1 at 0 oC and W2 at T oC. The coefficient of cubical expansion of metal is less than that of alcohol. If the density of the metal is large compared to that of alcohol, then

(a)W1>W2

(b) W1 = W2

(c) W1 < W2

(d) W2 = W1/2

A metal piece weighs 100 gm in air. It weighs 68 gm when immersed in a liquid at 10 oC and 69 gm in the same liquid at 22 oC.

Find the coefficient of linear expansion of the metal.

Given,

Density of liquid at 10 oC = 1.24 gm / cc and at 22 oC = 1.20 gm / cc

A solid floats on a liquid. The coefficients of volume expansion of the solid and liquid are and respectively. If their temperature is increased by DT, the fraction of the volume of solid submerged in liquid change by a factor

At 0 oC, the densities of wood and benzene are respectively 880 kg/m3 and 900 kg/m3. The coefficient of volume expansion of wood is 1.3 x 10-3 / oC and that of benzene is 1.5 x 10-3 / oC. Find the temperature at which a piece of wood will just sink in benzene.

A metal cube of coefficient of linear expansion a is floating in a liquid of coefficient of volume expansion g. When the temperature is raised by DT, the depth upto which the cube is submerged in the liquid remains unchanged. If the expansion of container is ignored, the relation between a and g is

A flask is completely filled with mercury and is sealed off at 10 oC.

Find the pressure within the flask at 160 oC.

Ignore the expansion of the glass.

Bulk modulus for mercury, B = 2500 MPa.

Co-efficient of volume expansion, g = 18.2 ? 10-5 / oC

A uniform solid sphere of radius Ro and mass M is set spinning with angular speed wo about a diameter. If its temperature is now increased without disturbing the sphere, what will be its new

a) angular speed and

b) rotational kinetic energy ?

An ice cube of mass 0.1 kg is placed in an isolated container which is at 227 oC. The specific heat capacity Cc of the container varies with temperature T according to the relation Cc = A + BT, where A = 100 cal/kg K and B = 2 x 10-2 cal/kg K2.

If the final temperature of the container is 27 oC, find the mass of the container.

(Latent heat of fusion for water = 8 x 104 cal/kg, specific heat of water = 103 cal/kg k)

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