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A sealed cylinder contains a sample of ideal gas at a pressure of $2.0 \mathrm{~atm}$. The rms speed of the molecules is $v_0$. If the rms speed is then reduced to $0.90 v_0$, what is the pressure of the gas?

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As we know the temperature is based on the thermal equilibrium concept. Let we suppose that two systems are allowed to exchange energy. So, The net flow of energy is always from the system at high temperature to the system at the lowest temperature. As energy flows, the temperature of the two systems approach one another. When the temperature are the same, there is no longer any net flow of energy. So, the objects are now said to be in thermal equilibrium. Heat is define as the energy that flows between two objects or systems due to a temperature difference between them.

Thermodynamics consists of four main laws. Zeroth law of Thermodynamics:

If two objects are each in thermal equilibrium with a third object, then the two are in thermal equilibrium with one another. As we know, Without the zeroth law, it will be impossible to define temperature. We use more than one scale to measure the temperature. The conversion between the Fahrenheit degree and the Celsius degree is

$\begin{align*} \Delta T_{F} &= \Delta T_{C} \times 1.8 \mathrm{~^{\circ}F/^{\circ}C} + 32 \mathrm{~^{\circ}F} \end{align*}$

The conversion between the Celsius degree and the Fahrenheit degree is

$\begin{align*} T_{C} &= \dfrac{ T_{F} - 32 \mathrm{~^{\circ}F}}{ 1.8 \mathrm{~^{\circ}F/^{\circ}C} } \end{align*}$

The conversion between the Kelvin degree and the Celsius degree is

$\begin{align*} T &= T_{C} + 273.15 \end{align*}$

In this problem, we have to find the pressure of gas using the given information.

$\begin{align*} P_i&=2.0\ \text{atm}\\ (v_{rms})_i&=v_0\\ (v_{rms})_f&=0.90v_0 \end{align*}$

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