A soda can with 120000 Pa of pressure is heated from 240 K to 300K in hot water. What is the new pressure in the can?
A. 150000 Pa
B. 240000 Pa
C. 96000 Pa
D. 120000 Pa
Show your work, correct answers only plz.
To solve this problem, we can use the ideal gas law, which states:
\[PV = nRT\]
Where:
P = pressure (in Pa)
V = volume (in m^3)
n = number of moles of gas
R = gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
Assuming that the volume of the soda can remains constant, we can rewrite the ideal gas law as:
\[P_1/T_1 = P_2/T_2\]
In this case, the initial pressure and temperature are given as P_1 = 120000 Pa and T_1 = 240 K, respectively. The final temperature is T_2 = 300 K, and we need to find the final pressure P_2.
Plugging in the values into the equation:
\[P_2 = P_1 \cdot \frac{T_2}{T_1}\]
\[P_2 = 120000 \cdot \frac{300}{240} = 150000 \, \text{Pa}\]
Therefore, the new pressure in the can is 150000 Pa. The correct answer is A.
To calculate the new pressure in the can, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
In this case, we are given that the initial pressure (P₁) is 120000 Pa, the initial temperature (T₁) is 240 K, and the final temperature (T₂) is 300 K. We need to find the new pressure (P₂).
Since we are dealing with a sealed soda can, the volume remains constant, so we can rewrite the ideal gas law equation as P₁/T₁ = P₂/T₂.
Substituting in the given values, we have:
P₁/T₁ = P₂/T₂
120000 Pa / 240 K = P₂ / 300 K
To solve for P₂, we can rearrange the equation:
P₂ = (120000 Pa / 240 K) * 300 K
Calculating this expression:
P₂ = 120000 * (300/240) Pa
P₂ = 150000 Pa
Therefore, the new pressure in the can is 150000 Pa.
The correct answer is: A. 150000 Pa.
To find the new pressure in the can, we can use the ideal gas law formula, which states that the product of pressure (P), volume (V), and temperature (T) is equal to the product of the number of moles (n) of gas and the ideal gas constant (R):
PV = nRT
In this case, we are only interested in how the pressure changes as the temperature changes, so we can rearrange the formula to solve for the new pressure (P2) in terms of the initial pressure (P1) and the initial (T1) and final (T2) temperatures:
P2 = (P1 * T2) / T1
Given:
Initial pressure (P1) = 120,000 Pa
Initial temperature (T1) = 240 K
Final temperature (T2) = 300 K
Plugging these values into the formula, we get:
P2 = (120,000 * 300) / 240
P2 = 150,000 Pa
Therefore, the new pressure in the can, when heated from 240 K to 300 K, is 150,000 Pa.
The correct answer is A. 150,000 Pa.