# Claculating volume in an adiabatic container

• lapoin29
In summary, the problem involves finding the volume of steam needed to reach thermal equilibrium at 20 degrees C when combined with 25g of ice at -15 degrees C in an adiabatic container with a piston, given a constant external pressure of 1 bar. The steam is assumed to behave as an ideal gas and the molar heat capacities do not change with temperature. The relevant heat capacities and molar mass of water are provided.
lapoin29
25g of ice frozen at -15 degrees C is combined with an unknown volume of steam at 200 degress C in an adiabatic container one wall of which is an adiabatic frictionless and weightless piston. Initial pressure in the container equals constant external pressure of 1 bar.
CALCULATE the volume of steam necessary for the system to come to a thermal equilibrium at 20 degrees C. Assume that the steam behaves as an ideal gas and molar heat capacities do not change with temp.

## Homework Equations

steam(gas) Cp,m,gas=33.58 J/mol/K; water(liquid) Cp,m,liquid=75.3 J/mol/K; ice(solid) Cp,m,solid=37.98 j/mol/K; $$\Delta$$Hm,fusion = 6010 J/mol; Mh20=18 g/mol

## The Attempt at a Solution

I'm soooo confused i have absolutely no idea where to start which is my main issue here

. I'm assuming you have to use the heat capacities of each state (gas, liquid, solid) and the molar mass of water but i don't know how to apply them. Any help would be greatly appreciated. Thanks!

## 1. How is volume calculated in an adiabatic container?

The volume in an adiabatic container can be calculated using the ideal gas law, which states that the product of pressure and volume is equal to the product of the number of moles of gas, the universal gas constant, and the temperature. This can be written as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is the temperature in kelvins.

## 2. What is an adiabatic container?

An adiabatic container is a container that does not allow for the transfer of heat between its contents and the surrounding environment. This means that the temperature inside the container remains constant, allowing for the use of the ideal gas law to calculate volume.

## 3. How does an adiabatic container affect the calculation of volume?

The adiabatic container does not affect the calculation of volume directly, but it allows for the use of the ideal gas law to calculate volume since the temperature remains constant. Without an adiabatic container, there may be a transfer of heat between the contents and the surroundings, making it difficult to accurately calculate volume using the ideal gas law.

## 4. Can the volume in an adiabatic container change?

Yes, the volume in an adiabatic container can change as long as the temperature remains constant. This means that the pressure and number of moles of gas can change, resulting in a change in volume according to the ideal gas law.

## 5. What is the significance of calculating volume in an adiabatic container?

Calculating volume in an adiabatic container is significant because it allows for the determination of the amount of gas present inside the container, which can be useful for various scientific and industrial purposes. It also helps in understanding the behavior of gases under different conditions and can be used to make predictions about their behavior in other scenarios.

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