In a process, molar heat capacity of a diatomic gas is (10/3)R. When heat Q is supplied to the gas, find the work done by it.

Question

In a process, molar heat capacity of a diatomic gas is (10/3)R. When heat Q is supplied to the gas, find the work done by it. (A)  (3Q/4) (B)  (Q/4) (C)  (Q/2) (D)  (Q/3)

Tardigrade Admin · Accepted Answer

dQ = n (10/3) RdT dU = (5/2) nRdT (dQ/dU) = (4/3) ∴ dU = (3/4) Q ∴ dW = dQ - dU = Q - (3/4)Q= (Q/4)

Q. In a process, molar heat capacity of a diatomic gas is $\frac{10}{3} R$ . When heat Q is supplied to the gas, find the work done by it.

$\frac{3 Q}{4}$

$\frac{Q}{4}$

$\frac{Q}{2}$

$\frac{Q}{3}$

$d Q = n \frac{10}{3} R d T$
$d U = \frac{5}{2} n R d T$
$\frac{d Q}{d U} = \frac{4}{3} ∴ d U = \frac{3}{4} Q$
$∴ d W = d Q - d U$
$= Q - \frac{3}{4} Q = \frac{Q}{4}$

Q. In a process, molar heat capacity of a diatomic gas is 310​R. When heat Q is supplied to the gas, find the work done by it.

43Q​

4Q​

2Q​

3Q​