Question

70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from 30° C to 35° C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is
(a) 30 calories
(b) 50 calories
(c) 70 calories
(d) 90 calories
Figure

Answer 1

Option (b) is correct

Explanation:

Step 1:

Because it takes 70 calories of heat to raise the temperature of 2 mole of an ideal gas at constant pressure from 30 ° C to 35 ° C. Often, heat variable at constant pressure,

$C_{p}=\frac{\Delta Q}{n \Delta T}$

$C_{p}=\frac{70}{2 \times(35-30)}$

$C_{p}=\frac{70}{2 \times 5}$

$C_{p}=\frac{70}{10}$

$C_{p}=7 \text { calories }-\frac{m o l^{-1}}{K}$

Step 2:

By ideal gas

$C_{p}-C_{v}=R=8.314 J-\frac{m o l^{-1}}{K} \simeq 2 \text { calories } \frac{m o t^{-1}}{\kappa}$

$\begin{aligned}&C_{v}=(7-2) \text { calories }-m o l^-^1 K^-^1\\&C_{v}=5 \text { calories }-m o l^-^1 K^-^1\end{aligned}$

$C_{v}=\frac{\Delta Q}{n \Delta T}$

$5=\frac{\Delta Q}{2 \times(35-30)}$

∆Q=5×2×(35-30)  

∆Q=5×2×5  

∆Q=50 calories  

Therefore, to raise the temperature of 2 moles of gas from  30 ° C to 35 ° C  to a constant volume, 50 calories must be supplied.

Answer 2

${\bold{\huge{\red{\underline{\green{ANSWER}}}}}}$

option B is correct ☺❤❤❤ ....