Solving 1.5 Moles Monatomic Ideal Gas at 314K - No Calc

• cdymdcool
In summary, the equation used to solve for the volume of a monatomic ideal gas at a given temperature and moles is V=nRT/P, where V is the volume, n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and P is the pressure. The ideal gas constant, R, has a value of 8.314 J/mol·K and can be derived from the equation PV=nRT. It is possible to solve for the volume of a monatomic ideal gas without knowing the pressure by rearranging the equation and solving for P first. To convert temperature from Celsius to Kelvin, simply add 273.15 to the Celsius temperature. The units of measurement for volume of
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1. 1.5 moles of a monatomic ideal gas is enclosed at 314K. THe initial volume of the gas is 3m^3. The gas is comperssed isothermally to a final volume of 1m^3. How much heat is removed from the gas.

So deltaU=0, Q=-W, So we have to know the area under the P-V curve, but how can we get the solution without calculus?

We can't. Algebra-based textbooks just provide the appropriate equation and justify it by saying that it can obtained by using calculus.

One possible approach to solving this problem without using calculus would be to use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. We can rearrange this equation to solve for pressure (P = nRT/V), and then use this pressure value to calculate the work done on the gas during compression (W = PΔV). Since the process is isothermal, we know that the change in internal energy (ΔU) is equal to zero, and therefore the heat removed from the gas (Q) must be equal to the work done on the gas (Q = -W). By plugging in the known values for n, T, and the initial and final volumes, we can solve for the heat removed from the gas.

1. What is the equation used to solve for the volume of 1.5 moles of a monatomic ideal gas at 314K without using a calculator?

The equation used to solve for the volume of a monatomic ideal gas at a given temperature and moles is V=nRT/P, where V is the volume, n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and P is the pressure.

2. How do you determine the value of the ideal gas constant in the equation for solving 1.5 moles of a monatomic ideal gas at 314K?

The ideal gas constant, R, has a value of 8.314 J/mol·K. This value is derived from the equation PV=nRT, where P is pressure, V is volume, n is number of moles, and T is temperature.

3. Can you solve for the volume of a monatomic ideal gas without knowing the pressure?

Yes, you can still solve for the volume of a monatomic ideal gas without knowing the pressure. You will need to rearrange the equation to solve for P, which is P=nRT/V. Once you have solved for P, you can use the value in the original equation to solve for the volume.

4. How do you convert temperature from Celsius to Kelvin in order to solve for the volume of a monatomic ideal gas?

To convert temperature from Celsius to Kelvin, you simply add 273.15 to the Celsius temperature. In this case, you would add 273.15 to 314°C to get 587.15K.

5. What are the units of measurement for the volume of a monatomic ideal gas?

The units of measurement for volume of a monatomic ideal gas are typically in liters (L) or cubic meters (m³), depending on the given units of pressure and temperature in the equation.

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