What happens to the pressure of a sample of helium gas if the temperature is increased from 200 K to 800 K, with no change in volume?

Explanation

Option A: The pressure of the gas will increase by a factor of 4.This is because the ideal gas law states that the pressure of a gas is directly proportional to its temperature, if the volume is held constant. So, if the temperature is increased by a factor of 4, the pressure will also increase by a factor of 4.Here is the equation for the ideal gas law:PV = nRTwhere:P is the pressure of the gasV is the volume of the gasn is the number of moles of gasR is the universal gas constant T is the temperature of the gasIf we keep the volume (V) and the number of moles of gas (n) constant, and increase the temperature (T) by a factor of 4, then the pressure (P) will also increase by a factor of 4.Therefore, the pressure of the gas will increase from 1 atmosphere to 4 atmospheres. Option B: This is not correct. The pressure of a gas can only decrease if the volume is increased or the number of moles of gas is decreased. In this case, the volume is held constant and the number of moles of gas is also held constant. So, the pressure cannot decrease. Option C: This is not correct. The pressure of a gas can only decrease by a factor of 2 if the volume is doubled or the number of moles of gas is halved. In this case, the volume is held constant and the number of moles of gas is also held constant. So, the pressure cannot decrease by a factor of 2. Option D: This is not correct. The pressure of a gas can only increase by a factor of 2 if the temperature is doubled. In this case, the temperature is increased by a factor of 4, so the pressure will increase by a factor of 4, not 2. Option E: This is not correct. The pressure of a gas will only remain constant if the temperature, volume, and number of moles of gas are all held constant. In this case, the temperature is increased, so the pressure will also increase.