What was the initial temperature of the gas in a closed cylinder if, after heating to 14 ° C, the pressure increased by 5%?

Since the change in gas temperature and pressure occurs in a closed cylinder, the process is isochoric and the ratio is correct:

Р1 / Т1 = Р2 / Т2, where according to the condition Р2 = 1.05Р1 (gas pressure increased by 5% (0.05)); Т2 = Т1 + 14 (after heating the temperature increased by 14 ºC).

Let’s determine the initial temperature:

P1 / T1 = P2 / T2 = 1.05P1 / (T1 + 14).

1 / T1 = 1.05 / (T1 + 14).

T1 + 14 = 1.05T1.

0.05T1 = 14.

T1 = 14 / 0.05 = 280 K (7 ºC).

Answer: The initial temperature was 280 K or 7 ºC.