We give 70 J as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase?

50 Joule

Explanation:

Diatomic gas

Q = Heat given = 70 J

n = number of moles

Cp = specific heat at constant pressure

ΔT = Change in temperature

R = Gas constant

Change in energy

ΔE = Q-w

⇒ΔE = n (Cp) ΔT-nRΔT

As it is a diatomic gas Cp = (7/2) R

Putting the value of Cp in the above equation we get

Q = (7/2) RΔT

ΔE = (5/2) RΔT

Dividing the equations we get

ΔE/Q = 5/7

⇒ΔE = (5/7) Q

⇒ΔE = (5/7) * 70

⇒ΔE = 50 J

∴ The internal energy change is 50 Joule