Question

21 J of heat energy is supplied to a diatomic ideal gas at constant pressure, then change in internal energy of the gas is
An : (3)
Please explain your answer

Answer 1

Answer:

15 J

Explanation:

Q=nCvT

U=nCpT

Q/U=Cv/Cp

21/U=7/5

U=15

Answer 2

Answer:

The change in internal energy of the gas is 15 J.

Explanation:

Given that,

Heat energy = 21 J

We need to calculate the value of nRdT

Using first law of thermodynamic

$dQ=dU+dW$

Put the value of dU and dW

$dQ=n\dfrac{f}{2}RdT+PdV$

$dQ=n\dfrac{f}{2}RdT+nRdT$

$dQ=nRdT(\dfrac{f}{2}+1)$

$dQ=nRdT(\dfrac{5}{2}+1)$

Here, f for diatomic, f = 5

$dQ=nRdT\times\dfrac{7}{2}$

Put the value in the equation

$nRdT=dQ\times\dfrac{2}{7}$

$nRdT=21\times\dfrac{2}{7}$

$nRdT=6$

We need to calculate the change in internal energy of the gas

Using formula of change in internal energy

$\Delta U=n\dfrac{f}{2}RdT$

Put the value into the formula

$\Delta U=\dfrac{5}{2}\times6$

$\Delta U=15\ J$

Hence, The change in internal energy of the gas is 15 J.