Question

A triatomic, diatomic and monoatomic gas are supplied with the same amount of heat at a constant pressure. Then:

• A. Fraction of energy used to change internal energy for maximum in monoatomic gas.
• B. Fraction of energy used to change internal energy is maximum for diatomic gas.
• C. Fraction of energy used to change internal energy is maximum for triatomic gas.
• D. Fraction of energy used to change internal energy is same for all the three gases.

Answer 1

The correct option is C Fraction of energy used to change internal energy is maximum for triatomic gas.

Since we know that heat supplied at constant pressure is given by $\Delta Q=n{C}_P\Delta T$
Energy required to change internal energy $\Delta U=n{C}_V\Delta T$
So, the fraction of energy required to change the internal energy of a gas is
$\frac{\Delta U}{\Delta Q}=\frac{n{C}_V\Delta T}{n{C}_P\Delta T}=\frac{C_V}{C_P}=\frac{1}{\gamma }$
we know that, ${\gamma }_{mono}=\frac{5}{3};{\gamma }_{dia}=\frac{7}{5};{\gamma }_{tria}=\frac{4}{3}$
Thus we get,
${\left(\frac{\Delta U}{\Delta Q}\right)}_{\text{mono}}=\frac{1}{{\gamma }_{\text{mono}}}=\frac{3}{5}$
${\left(\frac{\Delta U}{\Delta Q}\right)}_{dia}=\frac{1}{{\gamma }_{dia}}=\frac{5}{7}$
${\left(\frac{\Delta U}{\Delta Q}\right)}_{tria}=\frac{1}{{\gamma }_{tria}}=\frac{3}{4}$
Fraction of energy used to change internal energy is maximum in triatomic gas.
Hence, option (c) is the correct answer.