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 temperature and inversely proportional to pressure. From the given information, we can calculate the constant of proportionality as follows:

V/P = k/T

where k is a constant. Rearranging this equation, we get:

V = k(P/T)

Taking the partial derivative of V with respect to T and P, we get:

∂V/∂T = -k(P/T^2) and ∂V/∂P = k(1/T)

Substituting the given values T = 260 and P = 700, we get:

k = V(260)/(700) = 0.3726 L mmHg/K

Using this value of k, we can calculate the required values as follows:

∂V/∂T = -0.3726(700)/(260^2) = -0.0064 L/K

∂V/∂P = 0.3726(1/260) = 0.0014 L/mmHg

Therefore, the volume increases by 0.0064 L when the temperature decreases by 1 degree (beyond 260 K) and the pressure is fixed at 700 mm of mercury. The volume increases by 0.0014 L when the pressure increases by 1 mm of mercury (beyond 700 mm) and the temperature is fixed at 260 K. Hence, the best choice is D.

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