Heat and Thermodynamics 6 Question 24
29. 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 …….. ${ }^{\circ} C$.
$(1997,1 M)$
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Answer:
Correct Answer: 29. $45.68^{\circ}$
Solution:
- The gas thermometer works at constant volume. Therefore,
$$ \begin{aligned} & T \propto p \\ & \text { or } \quad T _2 / T _1=p _2 / p _1 \\ & \text { or } \quad T _2=T _1\left(p _2 / p _1\right) \\ & \text { or } \quad T _2=(273.16)\left(\frac{3.5 \times 10^{4}}{3 \times 10^{4}}\right) K \\ & =318.68 K \end{aligned} $$
or temperature at given pressure will be
$(318.68-273)^{\circ} C$
$$ \text { or } \quad 45.68^{\circ} C $$
