Answer:
The rate of change of the temperature is 0.0365 Kelvin per minute.
Explanation:
<u>Step 1</u>: Given data
ideal gas law: P*V = n*R*T
with P= pressure of the gas ( in atm) = 9.0 atm
with V= volume of the gass (in L) =12L
with n = number of moles = 10 moles
R = gas constant = 0.0821 L*atm* K^−1*mo^−1
T = temperature = TO BE DETERMINED
The volume decreases with a rate of 0.17L/min = dV/dT = -0.17
The pressure increases at a rate of 0.13atm/min = dP/dT
<u>Step 2:</u> The ideal gas law
P * [dV/dT] + V * [dP/dT] = nR * dT/dt
9 atm * (-0.17L/min) + 12L * 0.13atm/min = 10 moles * 0.0821 L*atm* K^−1*mo^−1 *dT/dt
0.03 = 0.821 * dT/dt
dT/dt = 0.03/0.821
dT/dt = 0.0365
Since the gas constant is expressed in Kelvin and not in °C, this means that <u>the rate of chagnge of the temperature is 0.0365 Kelvin per 1 minute.</u>
