What is the increase in temperature necessary for a hydrogen gas, initially at 0°C, to increase its volume by 5% at constant pressure?
Do you assume H2 is an ideal gas? (V1/T1) = (V2/T2)
For V1 use ANY convenient number, say 100 mL. Then for V2 you use 105. T1 is 273; T2 will be in kelvin.
Why did the hydrogen gas go on a diet? Because it wanted to expand its volume by 5%! *Ba dum tss* But in all seriousness, to answer your question, we can use Charles's Law to find the increase in temperature. Charles's Law states that at constant pressure, the volume of a gas is directly proportional to its temperature. Since the initial temperature is 0°C, we can convert it to Kelvin by adding 273.15 to get 273.15 K. Now let's do some calculations! If a 5% increase in volume is desired, we can use the formula (Vf - Vi) / Vi = 5% (or 0.05). Plugging in the values, we get (Vf - Vi) / Vi = 0.05. Since pressure is constant, we can say that Vf / Vi = Tf / Ti. Rearranging the equation, we get Tf = Ti * (Vf / Vi). Plugging in the values, we find Tf = 273.15 K * (1 + 0.05) = 273.15 K * 1.05. So the increase in temperature necessary would be approximately 286.81 K. Voila!
To calculate the increase in temperature necessary for a hydrogen gas, initially at 0°C, to increase its volume by 5% at constant pressure, you can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin) at constant pressure.
First, convert the initial temperature from Celsius to Kelvin:
T(initial) in Kelvin = T(initial in Celsius) + 273.15
T(initial) in Kelvin = 0 + 273.15 = 273.15 K
Next, calculate the final volume:
V(final) = V(initial) × (1 + 5%)
V(final) = V(initial) × (1 + 0.05)
Since the pressure is constant, we can assume that the ratio of V(initial) to V(final) is the same as the ratio of T(initial) to T(final):
V(initial) / V(final) = T(initial) / T(final)
Substituting the values we have:
V(initial) / V(initial) × (1 + 0.05) = T(initial) / T(final)
(1 + 0.05) = T(initial) / T(final)
Rearranging the equation to solve for T(final):
T(final) = T(initial) / (1 + 0.05)
T(final) = 273.15 K / 1.05
Calculating T(final):
T(final) ≈ 260.14 K
Therefore, the increase in temperature necessary for a hydrogen gas, initially at 0°C, to increase its volume by 5% at constant pressure, is approximately 260.14 K.
To determine the increase in temperature necessary for a hydrogen gas to increase its volume by 5% at constant pressure, we need to use Charles's Law, which states that for a given amount of gas at a constant pressure, the volume of the gas is directly proportional to its temperature.
Here's how we can approach this problem:
Step 1: Convert the initial temperature from Celsius to Kelvin.
To convert Celsius to Kelvin, we add 273.15 to the Celsius value.
Initial temperature in Kelvin = 0 + 273.15 = 273.15 K
Step 2: Calculate the final volume.
Since the volume increases by 5%, we can calculate it using the formula:
Final volume = Initial volume + (5% of Initial volume)
Note that we are assuming the pressure is constant.
Step 3: Calculate the final temperature.
Next, we can use Charles's Law to calculate the final temperature using the formula:
Final temperature = (Final volume / Initial volume) * Initial temperature
Let's plug in the values and calculate the final temperature:
Assuming the initial volume is V0 and the final volume is Vf:
Vf = V0 + (5/100) * V0 = V0 + 0.05V0 = 1.05V0 (since 5% is equal to 0.05)
Final temperature = (Vf / V0) * Initial temperature = (1.05V0 / V0) * 273.15 K
Simplifying the expression:
Final temperature = 1.05 * 273.15 K = 286.81 K
Therefore, the increase in temperature necessary for a hydrogen gas, initially at 0°C, to increase its volume by 5% at constant pressure is approximately 13.81 K (or 13.81°C).