Using the ideal gas law, we know that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature. Since the pressure and amount of gas are not changing, we can rewrite the equation as V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature. Let's plug in the given values:
V1 = 46.0 L
T1 = 400 K
T2 = 500 K
V1/T1 = V2/T2
46.0/400 = V2/500
Cross-multiplying:
400V2 = 23,000
Dividing both sides by 400:
V2 = 57.5 L
Rounding to three significant figures, the new volume is 57.5 L.