Q: A bakelite beaker has volume capacity of 500 cc at 30 °C .When it is partially filled with volume V_{m} at 30°C of mercury . , it is found that the unfilled volume of the beaker remains constant as the temperature is varied . If γ_{beaker} = 6 × 10^{-6}/°C and γ_{mercury} = 1.5 × 10^{-4}/°C , where γ is the coefficient of volume expansion , then V_{m} in cc is close to ……

**Click to See Solution : **

Sol: Given V = 500 cc , T = 30 °C

γ_{beaker} = 6 × 10^{-6}/°C

and γ_{mercury} = 1.5 × 10^{-4}/°C

V – V_{m} = V’ – V_{m}‘

Now , V’ = V(1 + γ_{b} ΔT)

and , V_{m}‘ = V_{m}(1 + γ_{m} ΔT)

V – V_{m} = V + V γ_{b} ΔT – V_{m} – V_{m} γ_{m} ΔT)

$\displaystyle V_m = V \frac{\gamma_b}{\gamma_m}$

$\displaystyle V_m = 500 \times \frac{6 \times 10^{-6}}{1.5 \times 10^{-4}}$

V_{m} = 20 cc