Solve the equation for the indicated variable. $$ P V=n R T ; \text { for } T $$

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UpStudy AI · Accepted Answer

To solve the equation $$ P V = n R T $$ for the variable $$ T $$, follow these steps:

**Given Equation:**
$$
P V = n R T
$$

**Objective:**
Solve for $$ T $$.

**Steps:**

1. **Isolate $$ T $$ on one side of the equation.**

Start with:
   $$
   P V = n R T
   $$

2. **Divide both sides of the equation by $$ n R $$ to solve for $$ T $$:**
   $$
   T = \frac{P V}{n R}
   $$

**Final Solution:**
$$
T = \frac{P V}{n R}
$$

**Where:**
- $$ P $$ = Pressure
- $$ V $$ = Volume
- $$ n $$ = Number of moles
- $$ R $$ = Ideal gas constant
- $$ T $$ = Temperature

This formula allows you to calculate the temperature $$ T $$ of an ideal gas when the pressure $$ P $$, volume $$ V $$, number of moles $$ n $$, and the ideal gas constant $$ R $$ are known.
To solve for $$ T $$ in the equation $$ P V = n R T $$, divide both sides by $$ n R $$. The solution is: $$ T = \frac{P V}{n R} $$

Solve the equation for the indicated variable. \[ P V=n R T ; \text { for } T \]

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