Question

In a constant volume gas thermometer the gas pressure at 0 degree Celsius is 200mmHg and at 100 degree Celsius it is 270mmHg what is the temperature if the thermometer produces a pressure of 214mmHg

Answer 1

Solution:

$p_1=200mmHg;$

$t_1=0^oC;$

$p_2=270mmHg;$

$t_2=100^oC;$

$V=const;$

$p=214mmHg;$

$t-?;$

what is the temperature if the thermometer produces a pressure of 214mmHg:

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

$\dfrac{\Delta p}{\Delta t}=\dfrac{270mmHg-200mmHg}{100^oC-0^oC}=0.7\dfrac{mmHg}{^oC};$

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

$t-t_1=\dfrac{214mmHg-200mmHg}{0.7\dfrac{mmHg}{^oC}}=20^oC;$

$t=20^oC+0^oC=20^oC;$

Answer:

 $t=20^oC;$