Ideal Gas Law Change Rate Problem

In summary, the gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. At a certain instant where P = 9.0 atm and V = 13 L, with P increasing at a rate of 0.15 atm/min and V decreasing at a rate of 0.16 L/min, the rate of change of T with respect to time can be found by taking the derivative of PV = nRT and substituting in the given values. The resulting equation is dT/dt
  • #1
Kurani
6
0

Homework Statement


The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 9.0 atm and is increasing at a rate of 0.15 atm/min and V = 13 L and is decreasing at a rate of 0.16 L/min. Find the rate of change of T with respect to time at that instant if n = 10 mol. (Round your answer to four decimal places.)


Homework Equations


PV=nRT
dT/dt = ___ K/min


The Attempt at a Solution


I was doing this problem on Web Assign and took the derivative of PV=nRT to get dT/dt=(PV'+VP')/nR and substituted in dT/dt=(9*.16+13*.15)/(10*.0821) and got 4.12911 but web assign doesn't accept it. I am not sure what I'm doing wrong. Thank you to anyone that can point me in the right direction.
 
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  • #2
Hint: The volume V is decreasing.
 
  • #3
lol, thanks a lot
 

Related to Ideal Gas Law Change Rate Problem

1. What is the Ideal Gas Law and how is it used to solve change rate problems?

The Ideal Gas Law is a fundamental equation in thermodynamics that describes the behavior of gases. It is written as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. This equation can be used to solve change rate problems by manipulating the variables to determine how changes in pressure, volume, temperature, or number of moles affect each other.

2. What are the units for the variables in the Ideal Gas Law?

The units for the variables in the Ideal Gas Law are pressure (P) in Pascals (Pa), volume (V) in cubic meters (m3), number of moles (n) in moles (mol), ideal gas constant (R) in Joules per mole-Kelvin (J/mol-K), and temperature (T) in Kelvin (K).

3. How can I determine the change rate of a gas using the Ideal Gas Law?

To determine the change rate of a gas, you will need to know two of the variables (pressure, volume, temperature, or number of moles) and solve for the third using the Ideal Gas Law. Then, you can compare the values before and after the change to determine the change rate. For example, if you know the initial pressure and volume of a gas, and then the final volume after a change, you can plug in the initial and final values into the Ideal Gas Law, solve for the final pressure, and calculate the change in pressure.

4. What are the assumptions made in the Ideal Gas Law?

The Ideal Gas Law makes several assumptions about gases, including that they are made up of tiny particles that have no volume or intermolecular forces, and that collisions between particles and with the container walls are perfectly elastic. These assumptions are not always true in real gases, but the Ideal Gas Law is still a useful approximation for many situations.

5. Can the Ideal Gas Law be used for all gases?

The Ideal Gas Law can be used for most gases at low pressures and high temperatures. However, at high pressures or low temperatures, the Ideal Gas Law may not accurately predict the behavior of real gases. In these cases, more complex equations, such as the Van der Waals equation, may be used instead.

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