Question

A gas thermometer is used as a standard thermometer for measurement of temperature. When the gas container of the thermometer is immersed in water at its triple point $273.16$K, the pressure in the gas thermometer reads $3.0\times {10}^4$ $N/m^2$. When the gas container of the same thermometer is immersed in another system, the gas pressure reads $3.5\times {10}^4$ $N/m^2$. The temperature of this system is therefore __________ ${}^{o}C$.

• A. ${60}^o$C.
• B. ${45.53}^o$C.
• C. ${53}^o$C.
• D. ${33}^o$C.

Answer 1

Answer: (B)

${45.53}^o$C.

$\text{Given}:$ $T_1=273.16K$, $P_1=3.0\times {10}^{4}N/m^2$, $P_2=3.5\times {10}^{4}N/m^2$

$\text{Solution}:$

In case of gas thermometer, the volume of the gas container remains constant.

$\therefore \frac{P_1}{T_1}=\frac{P_2}{T_1}$

$⟹\frac{3\times {10}^4}{273.16}=\frac{3.5\times {10}^4}{T_2}$

$⟹T_2=318.6K={45.53}^{o}C$

$\text{Hence B is the correct option}$