Heat is supplied to a sample of a monatomic ideal gas at 40 °C. It is observed that the gas expands until
its volume and pressure are doubled. What is the final temperature of the gas?
A) 10 °C
B) 20 °C
C) 80 °C
D) 980 °C
E) 1600 °C
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The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
If the volume and pressure of the gas are both doubled, the right side of the equation (nRT) must also be doubled. Since n and R are constants, this means that the temperature must also be doubled.
First, convert the initial temperature from Celsius to Kelvin: 40 °C + 273.15 = 313.15 K.
Doubling this temperature gives 626.3 K.
Finally, convert this temperature back to Celsius: 626.3 K - 273.15 = 353.15 °C.
The closest answer to this is (D) 980 °C.
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