Question

A monoatomic gas is taken in a vessel fitted with a light movable piston. If $50cal$ of heat is supplied to $2$ moles of gas then its rise in temperature will be $\left(R=2cal/mol-K\right)$

• A. $50K$
• B. $5K$
• C. $10K$
• D. $20K$

Answer 1

The correct option is B

$5K$

Step 1: Given

Amount of heat: $Q=50cal$

Number of moles: $n=2$

$R=2cal/mol-K$

Specific heat capacity is C_p

Step 2: Formula used

$C_p=\frac{5}{2}R$

$Q=n{C}_{p}dT$

Step 3: Solution

Calculate the specific heat capacity by substituting the value of R

$$\begin{gathered} C_p=\frac{5}{2}R \\ =\frac{5}{2}\times 2 \\ =5J/kg-K \end{gathered}$$

Substitute all the values in the formula $Q=n{C}_{p}dT$

$$\begin{gathered} 50=2\times 5dT \\ 50=10dT \\ \Rightarrow dT=\frac{50}{10} \\ \Rightarrow dT=5K \end{gathered}$$

Hence, the rise in temperature is 5 K.

Thus option (B) is correct.