Question

How will the volume of a fixed sample of gas change if the pressure is doubled and its Celsius temperature is halved? How will the volume of a fixed sample of gas change if the pressure is doubled and its Celsius temperature is halved? The change cannot be determined without more specific information.

A. It will decrease by a factor of 4.
B. It will decrease by a factor of 2.
C. It will double.
D. It will remain constant.

Answer 1

The volume of a fixed sample of gas will decrease by a factor of 4 if the pressure is doubled and its Celsius temperature is halved. Hence the correct answer is option A

Step-by-step explanation:

The volume of a fixed sample of gas will decrease if the pressure is doubled and its Celsius temperature is halved. According to Boyle's law, when the pressure of a gas is doubled at a constant temperature, the volume of the gas will be halved. Additionally, when the temperature of a gas is halved at a constant pressure, the volume of the gas will also be halved, according to Charles's law.

Therefore, when both the pressure is doubled and the temperature is halved, the volume of the gas will be halved twice, resulting in a decrease by a factor of 4. So, the correct answer is option A: It will decrease by a factor of 4.

Hence the correct answer is option A

Answer 2

Answer: The volume will decrease by a factor of 4.

Step-by-step explanation:

To calculate the volume when temperature and pressure has changed, we use the equation given by combined gas law.

The equation follows:

`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

where,

`P_1,V_1\text{ and }T_1` are the initial pressure, volume and temperature of the gas

`P_2,V_2\text{ and }T_2` are the final pressure, volume and temperature of the gas

We are given:

`P_1=P_1\\V_1=V_1\\T_1=T_1\\P_2=2P_1\\V_2=?\\T_2=(T_1)/(2)`

Putting values in above equation, we get:

`(P_1* V_1)/(T_1)=(2P_1* V_2)/((T_1)/(2))\\\\V_2=(P_1* V_1)/(T_1)* (T_1)/(4P_1)\\\\V_2=(V_1)/(4)`

Hence, the volume will decrease by a factor of 4.