# During the day at 27°C a cylinder with a sliding top contains 20.0 liters of air. At night it only holds 19 liters. What is the temperature at night? Give the answer in Kelvin and °C?

Jul 9, 2014

The temperature at night is 290 K or 10 °C.

This is an example of a Charles' Law problem. See

http://socratic.org/questions/what-is-charles-law

${V}_{1}$ = 20.0 L; ${T}_{1}$ = (27 + 273.15) K = 300 K
${V}_{2}$ = 19 L; ${T}_{2}$ = ?

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

T_2 = T_1× V_2/V_1 = 300 K × $\left(19 \text{L")/(20.0"L}\right)$ = "285.1" K = 290 K (2 significant figures)

285.1 K = (285.1 -273.15) °C = "12.0" °C = 10 °C (1 significant figure)

The temperature at night is 290 K or 10 °C.

This makes sense. The volume decreases by about 5 %, so the Kelvin temperature should also decrease by 5 % (about 15 K).

Note: The Kelvin temperature can have only two significant figures, because that is all you gave for the second volume.

The Celsius temperature can have only one significant figure, because the "8" in 285.1 is the last significant figure in that number. If you need more precision, you will have to recalculate.