Question

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied, which increases the internal energy of the gas, is

Answer 1

1. When heat is supplied to a gas at constant pressure, heat gets used up in order to increase the internal energy of the gas and also to increase volume (Expansion) to maintain constant pressure.
2. ΔQ=  ΔU + ΔW
3. Above equation in words can be written as
4. Heat supplied at constant pressure= work done/+ raise in internal energy
5. $Fraction of Energy = \frac{\triangle U}{\triangle Q_{p} } =\frac{C_{v} }{C_{p} } = \frac{1}{\gamma}$
6. But it is given that gas is diatomic.
7. γ =  7/5 for diatomic gases.
8. Hence fraction of energy = 5/7.

Answer : The answer is 5/7 of the energy supplied increases the internal energy.

Answer 2

The fraction of heat supplied is:

• Ideal diatomic gas is heated at constant pressure. This, in turn, increases the internal energy of the gas.
• Heat supplied =Q = n $C_p$ ΔT    ($C_p$ is used as pressure is constant)

                                      = n (3.5 R) ΔT

• ΔU = n $C_v$ ΔT = n (2.5 R) ΔT
• Fraction of the heat energy supplied = (ΔU/Q) =(2.5/3.5) = 5/7