Question

$2\text{kg}$ of air kept in closed vessel of volume $1{\text{m}}^3$ is heated from ${20}^{\circ }\text{C}$ to ${35}^{\circ }\text{C}$ at constant volume. What is the change in pressure of the air?

• A. $4.3\times {10}^3{\text{N/m}}^2$
• B. $10.4\times {10}^3{\text{N/m}}^2$
• C. $8.61\times {10}^3{\text{N/m}}^2$
• D. $6.2\times {10}^3{\text{N/m}}^2$

Answer 1

The correct option is C $8.61\times {10}^3{\text{N/m}}^2$

Characteristic gas constant for air
$R_C=0.287\times {10}^3\text{J/kg K}$
Also,
$PV=m{R}_{C}T$
Where $m=$ mass,
$\Rightarrow$ For constant volume,
$\left(\Delta P\right)V=m{R}_C\left(\Delta T\right)$
$\Delta T=35-20=15,V=1{\text{m}}^3$
Where $\Delta P=$ change in pressure
$\Rightarrow \Delta P=\frac{m{R}_C\Delta T}{V}$
$\Delta P=\frac{2\times 0.287\times {10}^3\times (35-20)}{1}$
$\therefore \Delta P=8.61\times {10}^3{\text{N/m}}^2$