Question

4. An industrial gas storage tank with adjustable pressure has volume of 100.0 L when the
gas temperature is 55.0°C. Calculate the temperature of the gas if the volume drops to
75.0 L with no loss in pressure.

Answer 1

Taking into account the Charles' law, the temperature of the gas if the volume drops to 75.0 L is 246 K or -27 C.

Charles' law

Charles' law establishes the relationship between the temperature and the volume of a gas when the pressure is constant. This law says that for a given sum of gas at constant pressure, as the temperature increases, the volume of the gas increases and as the temperature decreases, the volume of the gas decreases. That is, the volume is directly proportional to the temperature of the gas.

Mathematically, Charles' law is a law that says that when the amount of gas and pressure remain constant, the ratio between volume and temperature will always have the same value:

$\frac{V}{T}=k$

Considering an initial state 1 and a final state 2, it is fulfilled:

$\frac{V1}{T1}=\frac{V2}{T2}$

Final temperature

In this case, you know:

• V1= 100 L
• T1= 55 C= 328 K (being 0 C= 273 K)
• V2= 75 L
• T2= ?

Replacing in Charles's law:

$\frac{100 L}{328 K}=\frac{75 L}{T2}$

Solving:

$T2x\frac{100 L}{328 K}=75 L$

$T2=\frac{75 L}{\frac{100 L}{328 K}}$

T2= 246 K= -27 C

Finally, the temperature of the gas if the volume drops to 75.0 L is 246 K or -27 C.

Learn more about Charles' law:

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