We use the ideal gas law in terms of the Boltzmann constant:
\(PV = NkT\)
Where:
- \( P = 1.38 \, \text{atm} = 1.38 \times 1.01 \times 10^5 \, \text{Pa} \),
- \( N = 2.0 \times 10^{25} \) (total number of molecules),
- \( k = 1.38 \times 10^{-23} \, \text{J K}^{-1} \).
Rearranging the formula to solve for \( T \):
\(T = \frac{PV}{Nk}\)
Substituting the values:
\(P = 1.38 \times 1.01 \times 10^5 = 1.01 \times 10^5 \, \text{Pa}\)
\(T = \frac{1.01 \times 10^5}{2 \times 10^{25} \times 1.38 \times 10^{-23}}\)
Simplifying, we get:
\(T = \frac{1.01 \times 10^3}{2} \approx 500 \, \text{K}\)
Thus, the temperature \( T \) is 500 K.
The Correct Answer is: 500 K
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32