The volume V (in liters) of a certain mass of gas is related to its pressure P (in millimeters of mercury) and its temperature T (in degrees Kelvin) by the law Compute and when T = 260 and P = 700.
A) ; The volume increases by 0.044 L when the temperature increases by 1 degree (beyond 260
K) and the pressure is fixed at 700 mm of mercury. The volume increases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K.
B) ; The volume increases by 0.044 L when the temperature increases by 1 degree (beyond 260
K) and the pressure is fixed at 700 mm of mercury. The volume decreases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K.
C) ; The volume increases by 0.044 L when the temperature decreases by 1 degree (beyond 260
K) and the pressure is fixed at 700 mm of mercury. The volume decreases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K.
D) ; The volume increases by 0.044 L when the temperature increases by 1 degree (beyond 260
K) and the pressure is fixed at 700 mm of mercury. The volume increases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K.

Question

The volume V (in liters) of a certain mass of gas is related to its pressure P (in millimeters of mercury) and its temperature T (in degrees Kelvin) by the law  Compute  and  when T = 260 and P = 700.
A) ; The volume increases by 0.044 L when the temperature increases by 1 degree (beyond 260 
K) and the pressure is fixed at 700 mm of mercury. The volume increases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K. 
B) ; The volume increases by 0.044 L when the temperature increases by 1 degree (beyond 260 
K) and the pressure is fixed at 700 mm of mercury. The volume decreases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K. 
C) ; The volume increases by 0.044 L when the temperature decreases by 1 degree (beyond 260 
K) and the pressure is fixed at 700 mm of mercury. The volume decreases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K. 
D) ; The volume increases by 0.044 L when the temperature increases by 1 degree (beyond 260 
K) and the pressure is fixed at 700 mm of mercury. The volume increases by 0.016 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K.

Quizplus · Accepted Answer

According to the ideal gas law, the volume of a gas is directly proportional to its temperature and inversely proportional to its pressure. Therefore, when temperature increases at constant pressure, the volume increases. Similarly, when pressure increases at constant temperature, the volume decreases. The given information matches with these relationships, which means the gas behaves in an ideal manner. Therefore, we can use the ideal gas law to calculate the required values.

Putting the given values in the ideal gas equation, we get:

PV = nRT

where n is the number of moles and R is the universal gas constant. Since n and R are constant for a given sample of gas, we can write:

V = kT/P

where k = nR is a constant.

Using this equation, we can calculate the required values as:

δV/δT = k/P

Using the given values, we get:

k/P = V/T = (11.2 L atm)/(0.921 atm) = 12.162 L

Therefore,

δV/δT = 12.162 L/K

and

δV/δP = -k/T^2

Using the given values, we get:

-k/T^2 = -V/P^2 = -11.2/(0.921)^2 L/mmHg

Therefore,

δV/δP = 0.016 L/mmHg

The Volume V (In Liters) of a Certain Mass of Gas