JEE PYQ: Thermodynamics Question 16
Question 16 - 2020 (03 Sep Shift 1)
A bakelite beaker has volume capacity of 500 cc at 30$°$C. When it is partially filled with $V_m$ volume (at 30$°$C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $\gamma_{\text{(beaker)}} = 6 \times 10^{-6}$ $°$C$^{-1}$ and $\gamma_{\text{(mercury)}} = 1.5 \times 10^{-4}$ $°$C$^{-1}$, where $\gamma$ is the coefficient of volume expansion, then $V_m$ (in cc) is close to __________.
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Answer: 20
Solution
Volume capacity of beaker, $V_0 = 500$ cc
$V_b = V_0 + V_0 \gamma_{\text{beaker}} \Delta T$
When beaker is partially filled with $V_m$ volume of mercury,
$V_b’ = V_m + V_m \gamma_M \Delta T$
Unfilled volume $(V_0 - V_m) = (V_b - V_m’)$
$\Rightarrow V_0 \gamma_{\text{beaker}} = V_m \gamma_M$
$\therefore V_m = \frac{V_0 \gamma_{\text{beaker}}}{\gamma_M}$
$V_m = \frac{500 \times 6 \times 10^{-6}}{1.5 \times 10^{-4}} = 20$ cc.
BETA
