A movable piston having a mass of 8.00 kg and a cross-sectional area of 5.00 cm2 traps 0.200 moles of an ideal gas in a vertical cylinder. If the piston slides without friction in the cylinder, how much work is done on the gas when its temperature is increased from 18°C to 308°C?

Well, that's a hot topic! Let's calculate the work done on the gas, shall we?

First, we need to find the change in volume of the gas as its temperature increases. According to Gay-Lussac's law, at constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature.

So, let's convert the temperatures to Kelvin. 18°C is 18 + 273 = 291 K. And 308°C is 308 + 273 = 581 K.

We can calculate the change in volume using the ideal gas law:

(V2 - V1) = (nRT2 - nRT1) / P

Where:
n = number of moles = 0.200 moles
R = ideal gas constant = 8.314 J/(mol·K)
T1 = initial temperature in Kelvin = 291 K
T2 = final temperature in Kelvin = 581 K
P = pressure = force / area

Now, we need to find the pressure exerted on the piston. The pressure is equal to the weight of the piston divided by its area. The weight of the piston can be calculated using the formula:

weight = mass x acceleration due to gravity

So:
weight = 8.00 kg x 9.8 m/s^2 = 78.4 N

And the pressure:
P = weight / area

The area is given as 5.00 cm^2, which is equal to 0.0005 m^2. So:
P = 78.4 N / 0.0005 m^2 = 156800 Pa

Now, we substitute all the values into the equation to find the change in volume:
(V2 - V1) = (0.200 mol x 8.314 J/(mol·K) x (581 K - 291 K)) / 156800 Pa

After doing the math, we find (V2 - V1) = 0.012 m^3

The work done on the gas is given by the formula:
work = P x ΔV

So:
work = 156800 Pa x 0.012 m^3 = 1881.6 J

Therefore, the work done on the gas when its temperature increases from 18°C to 308°C is approximately 1881.6 Joules.

To find the work done on the gas when its temperature is increased, we can use the formula for work done in thermodynamics:

W = P(V2 - V1)

Where:
W is the work done,
P is the pressure exerted by the gas,
V2 is the final volume,
V1 is the initial volume.

To find the pressure exerted by the gas, we can use the ideal gas law:

PV = nRT

Where:
P is the pressure,
V is the volume,
n is the number of moles of gas,
R is the ideal gas constant,
T is the temperature in Kelvin.

First, we need to convert the initial and final temperatures from Celsius to Kelvin:

T1 = 18 + 273 = 291 K
T2 = 308 + 273 = 581 K

Next, we can calculate the initial and final volumes using the ideal gas law:

V1 = (nRT1)/P
V2 = (nRT2)/P

Since the piston is movable, the pressure stays constant throughout the process. Therefore, we can consider the pressure as a constant and cancel it out when calculating the work.

Now, let's calculate the initial and final volumes:

V1 = (0.200 moles * 8.314 J/(mol*K) * 291 K) / P
V2 = (0.200 moles * 8.314 J/(mol*K) * 581 K) / P

Now, we can substitute the values into the formula for work done:

W = P(V2 - V1)
= P(0.200 moles * 8.314 J/(mol*K) * 581 K / P - 0.200 moles * 8.314 J/(mol*K) * 291 K / P)
= 0.200 moles * 8.314 J/(mol*K) * (581 K - 291 K)

Calculating this expression gives us the work done on the gas when its temperature is increased from 18°C to 308°C.

To calculate the work done on the gas, we can use the formula:

W = P * A * Δh

Where:
W is the work done on the gas (in Joules),
P is the pressure exerted by the gas (in Pascals),
A is the cross-sectional area of the piston (in square meters),
Δh is the change in height of the piston (in meters).

To find the pressure, we can use the ideal gas law:

PV = nRT

Where:
P is the pressure (in Pascals),
V is the volume of the gas (in cubic meters),
n is the number of moles of gas,
R is the ideal gas constant (8.314 J/(mol·K)),
T is the temperature of the gas (in Kelvin).

First, let's convert the cross-sectional area from square centimeters to square meters:
A = 5.00 cm^2 = 5.00 * 10^(-4) m^2

Next, let's convert the temperature from Celsius to Kelvin:
T1 = 18°C = 18 + 273 = 291 K
T2 = 308°C = 308 + 273 = 581 K

Now, we need to find the pressure at both temperatures.
Using the ideal gas law, we have:
P1 * V = n * R * T1
P2 * V = n * R * T2

Since the volume (V) and the number of moles (n) are constant, we can write:
P1 * T1 = P2 * T2

Solving for P1:
P1 = (P2 * T2) / T1

Now, we can calculate the pressure P1:
P1 = (P2 * T2) / T1

Next, we need to determine the change in height of the piston (Δh). Since the piston is movable, its change in height is related to the change in volume of the gas.

The change in volume can be calculated using the ideal gas law:
V1 = (n * R * T1) / P1
V2 = (n * R * T2) / P2

ΔV = V2 - V1
Δh = A * ΔV

Finally, we can calculate the work done on the gas:
W = P1 * A * Δh

Plug in the values above and solve for W to get the work done on the gas when its temperature is increased from 18°C to 308°C.