ThermodynamicsMedium

Ideal gas: temperature from PV = nRT

An ideal gas, n = 3 mol, occupies V = 8 L at pressure p = 8 atm. Find the temperature. (R = 8.314 J/mol·K, 1 atm = 101325 Pa)

Given data

n = 3 molV = 8 L = 0.008 m³p = 8 atm ≈ 8.11×10⁵ Pa

Steps

0 / 1

The gas is ideal, so pressure, volume and temperature are linked by the equation of state pV = nRT. You know p, V, n: the only unknown is T, so isolate T = pV/(nR). It is essential to use SI units (p in Pa, V in m³), otherwise R does not match.
Write your working — the numerical result must appear in the text K

Full worked solution

The gas is ideal, so pressure, volume and temperature are linked by the equation of state pV = nRT. You know p, V, n: the only unknown is T, so isolate T = pV/(nR). It is essential to use SI units (p in Pa, V in m³), otherwise R does not match.
$T = \frac{pV}{nR} = \frac{8.11\times10^5\cdot 0.008}{3\cdot 8.314}$
$T = \frac{6485}{24.94} \approx \mathbf{260\,K}$ (about −13 °C).

Result:

T \approx 260

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