Advertisements
Advertisements
प्रश्न
Prove the Mayer's relation `C_p - C _v = R/J`
Advertisements
उत्तर
Consider one mole of an ideal gas that is enclosed in a cylinder by a light, frictionless, airtight piston.
Let P, V, and T be the pressure volume and temperature of the gas, respectively. If the gas is heated so that its temperature rises by dT, but volume remains constant.
Let dQ1 → be the amount of heat supplied to the gas,
dE → be the increase in internal energy. Since, volume of gas is constant, no work is done in moving the piston.
dQ1 = dE + dW
∴ dQ1 = dE = CVdT ...(i)
(As dW = 0)
If the gas is heated to the same temperature at constant pressure.
Let dV → be the increase in volume.
Therefore work is done and it is given by
dW = PdV
Let dQ2 → be the heat supplied to the gas
∴ dQ2 = dE + dW
∴ CpdT = dE + dW ...(ii)
Putting dE = CvdT and dW = PdV
∴ Equation (ii) becomes
CPdT = CvdT + PdV
(Cp − Cv)dT = PdV ...(iii)
For one mole of gas
PV = RT
∴ pdV = RdT
∴ (Cp − Cv)dT = RdT
Cp − Cv = R ...(iv)
This is known as Mayer's relation.
Generally, heat supplied is measured in calories, and work done is measured in joules. Therefore, equation (iv) is modified as follows:.
`C_p - C _v = R/J`
APPEARS IN
संबंधित प्रश्न
Two metallic blocks P and Q of masses in ratio 2: 1 are given the same amount of heat. If their temperature rise by the same amount, compare their specific heat capacities.
Give one example where high specific heat capacity of water is used as cooling purposes?
Give one example where high specific heat capacity of water is used as heat reservoir ?
A mass m1 of a substance of specific heat capacity c1 at temperature t1 is mixed with a mass m2 of other substance of specific heat capacity c2 at a lower temperature t2. Deduce the expression for the temperature t of the mixture. State the assumption made, if any.
The S.I. unit of specific heat capacity is ______.
Name three fossil fuels that emit carbon dioxide into the atmosphere ?
What is meant by global warming?
The ratio of specific heat capacity to molar heat capacity of a body _____________ .
Indian style of cooling drinking water is to keep it in a pitcher having porous walls. Water comes to the outer surface very slowly and evaporates. Most of energy needed for evaporation is taken from the water itself and the water is cooled down. Assume that a pitcher contains 10 kg of water and 0.2 g of water comes out per second. Assuming no backward heat transfer from the atmosphere to the water, calculate the time in which the temperature decrease by 5°C. Specific heat capacity of water = 4200 J kg−1 °C−1 and latent heat of vaporization of water = 2.27 × 106 J kg−1.
104g of water at 30°C is taken in a calorimeter made of copper of mass 42 g. When a certain mass of ice at 0°C is added to it, the final steady temperature of the mixture after the ice has melted, was found to be 10°C. Find the mass of ice added. [Specific heat capacity of water = 4.2 Jg–1°C–1 ; Specific latent heat of fusion of ice = 336 Jg–1; Specific heat capacity of copper = 0.4 Jg–1°C–1] .
A burner raises the temperature of 360 g of water from 40°C to 100°C in 5 minutes. Calculate the rate of heat supplied by the burner.
Specific heat capacity of a substance A is 3.8 J g-1 K-1 and of substance B is 0.4 J g-1 k-1. Which substance is a good conductor of heat? How did you arrive at your conclusion?
Explain, Why is it advisabile to pour cold water over burns, caused on human body, by hot solids?
Discuss how high specific heat capacity of water helps in formation of land and sea breeze.
State factors on which the amount of heat radiated by a body depends.
Write the name.
The amount of heat absorbed at constant temperature by unit mass of a liquid to convert into gaseous phase.
Write a short note.
Specific heat capacity
Read this activity and answer the following questions.
- Take three spheres of iron, copper and lead. the lead of equal mass.
- Put all the three spheres in boiling water in the beaker for some time.
- Take the three spheres out of the water.
- All the spheres will be at a temperature 100 °C.
- Put them immediately on the thick slab of wax.
- Note, the depth that each of the sphere goes into the wax.
Questions:
- Which property is determined from this activity?
- Give name to that property.
- Explain the term principal of heat exchange with the help of this activity.
What is specific heat capacity?
Heat is applied to a rigid diatomic gas at constant pressure. The ratio ΔQ : ΔU : ΔW is ______.
For a gas `"R"/"C"_"v" = 0.4,` where 'R' is the universal gas constant and 'Cv' is molar specific heat at constant volume. The gas is made up of molecules which are ______.
If 'f' is the number of degrees of freedom of a molecule of a gas and ratio of molar specific heats of a gas, ϒ = 1 + `2/"f"` where ϒ = Cp/Cv. The ratio of 'ϒ' for monoatomic gas to 'ϒ' for (rigid) f diatomic gas is ______.
On supplying 100 µC of charge to a conductor, its potential rises by 5 V then capacity of the conductor is ______.
Find the odd one out:
In the method of mixtures, a hot metal is dropped into cold water and the mixture reaches a final temperature. Which principle is used to find the specific heat of the metal?
