Question

A constant volume gas thermometer records a pressure of 250mmHg at 0°c and 290mmHg at 100°c. Calculate the room temperature when the gas pressure is 262mmHg

Answer 1

Solution.

$p_1=250mmHg;$

$t_1=0^oC;$

$p_2=290mmHg;$

$t_2=100^oC;$

$V=const;$

$p=262mmHg;$

$t-?;$

Find the change in pressure when the temperature changes by 1^oC:

$\dfrac{\Delta p}{\Delta t}=\dfrac{p_2-p_1}{t_2-t_1};$

$\dfrac{\Delta p}{\Delta t}=\dfrac{290mmHg-250mmHg}{100^oC-0^oC}=0.4\dfrac{mmHg}{^oC};$

$\dfrac{\Delta p}{\Delta t}=\dfrac{p-p_1}{t-t_1};\implies t-t_1=\dfrac{p-p_1}{\dfrac{\Delta p}{\Delta t}};$

$t-t_1=\dfrac{262mmHg-250mmHg}{0.4\dfrac{mmHg}{^oC}}=30^oC;$

$t=30^oC+0^oC=30^oC;$

Answer: $t=30^oC;$