Question 378: Thermodynamics & KTG

Question

The amount of heat needed to raise the temperature of 4 moles of  rigid diatomic gas from 0$$^\circ$$ C to 50$$^\circ$$ C when no work is done is ___________. (R is the universal gas constant).

Accepted Answer

According to first law of thermodynamics,
$$\Delta$$Q = $$\Delta$$U + $$\Delta$$W ..... (i)
where, $$\Delta$$Q = quantity of heat energy supplied to the system, $$\Delta$$U = change in the internal energy of a closed system and $$\Delta$$W = work done by the system on its surroundings.
As per question, no work is done
$$	herefore$$ $$\Delta$$W = 0 ..... (iii)
From Eqs. (i) and (ii), we get
$$\Delta$$Q = 0 + $$\Delta$$U $$\Rightarrow$$ $$\Delta$$Q = $$\Delta$$U
or $$\Delta$$Q = $$\Delta$$U = nC
V
$$\Delta$$T
where,
C
V
= specific heat capacity at constant volume for diatomic gas = $${{5R} \over 2}$$
$$\Delta$$T = change in temperature = (50 $$-$$ 0) = 50$$^\circ$$C
n = number of moles = 4
$$\Rightarrow$$ $$\Delta$$Q = nC
V
$$\Delta$$T
= $$4 	imes {{5R} \over 2} 	imes (50)$$ = 500 R = 500 R

Answer

500 R

Answer

250 R

Answer

750 R

Answer

175 R

Thermodynamics & KTG

The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from 0$^\circ C to 50^\circ$ C when no work is done is ___________. (R is the universal gas constant).

Choose the correct answer: