In an empty rubber raft the pressure is approximately constant. You push on a large air pump that pushes 1.0 L(1.0× 10^−3m3) of air into the raft. You exert a 17N force while pushing the pump handle 3.0×10^−2m .
Determine the work done on the gas.
If all of the work is converted to thermal energy of the 1.0 L of gas, what is the temperature increase of the gas? Assume that the air obeys the ideal gas law and is initially at 293 K.
skeet
Part A) 17*(3.0*10^-2)
Part B) Still looking for an answer
To determine the work done on the gas, we can use the equation:
Work = Force x Distance
In this case, the force exerted is 17N, and the distance is 3.0×10^−2m. So the work done on the gas is:
Work = 17N x 3.0×10^−2m = 0.51 N.m or 0.51 Joules (J)
Now, to calculate the temperature increase of the gas, we need to use the ideal gas law formula:
PV = nRT
Where:
P = pressure of the gas (assumed to be constant)
V = volume of the gas (1.0 L or 1.0× 10^−3m3)
n = number of moles of the gas (we can calculate this using the ideal gas law)
R = universal gas constant (8.314 J/(mol·K))
T = temperature of the gas in Kelvin
First, we need to find the number of moles of the gas. We can use the equation:
n = V / Vm
Where Vm is the molar volume, which is the volume occupied by 1 mole of gas. For an ideal gas at standard temperature and pressure (STP), the molar volume is approximately 22.4 L/mol.
n = (1.0× 10^−3m3) / (22.4 L/mol) ≈ 4.46× 10^−5 moles
Now, we can rearrange the ideal gas law equation to solve for the temperature:
T = (PV) / (nR)
Using the given information:
P = constant pressure (unknown, but not needed for the calculation)
V = volume of gas (1.0 L or 1.0× 10^−3m3)
n = number of moles of gas (4.46× 10^−5 moles)
R = universal gas constant (8.314 J/(mol·K))
T = (PV) / (nR) = (unknown × 1.0× 10^−3m3) / (4.46× 10^−5 moles × 8.314 J/(mol·K))
Since the pressure is constant, we can further simplify the equation:
T = (P × 1.0× 10^−3m3) / (4.46× 10^−5 moles × 8.314 J/(mol·K))
Now, substitute the known values and solve for the temperature T:
T = (0.51 J) / (4.46× 10^−5 moles × 8.314 J/(mol·K))
T ≈ 1450 K (rounded to the nearest whole number)
Therefore, the temperature increase of the gas is approximately 1450 K.