Advertisements
Advertisements
Question
A gas cylinder has walls that can bear a maximum pressure of 1.0 × 106 Pa. It contains a gas at 8.0 × 105 Pa and 300 K. The cylinder is steadily heated. Neglecting any change in the volume, calculate the temperature at which the cylinder will break.
Advertisements
Solution
Given:-
Maximum pressure that the cylinder can bear, Pmax = 1.0 × 106 Pa
Pressure in the gas cylinder, P1 = 8.0 × 105 Pa
Temperature in the cylinder, T1 = 300 K
Let T2 be the temperature at which the cylinder will break.
Volume is constant. Thus, ............(Given)
V1= V2 = V
Applying the five variable gas equation, we get
\[\frac{P_1 V}{T_1} = \frac{P_2 V}{T_2} .........( \because V_1 = V_2 )\]
\[ \Rightarrow \frac{P_1}{T_1} = \frac{P_2}{T_2}\]
\[ \Rightarrow T_2 = \frac{P_2 \times T_1}{P_1}\]
\[ \Rightarrow T_2 = \frac{1 . 0 \times {10}^6 \times 300}{8 . 0 \times {10}^5}=375K\]
APPEARS IN
RELATED QUESTIONS
Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?
It is said that the assumptions of kinetic theory are good for gases having low densities. Suppose a container is so evacuated that only one molecule is left in it. Which of the assumptions of kinetic theory will not be valid for such a situation? Can we assign a temperature to this gas?
Is it possible to boil water at room temperature, say 30°C? If we touch a flask containing water boiling at this temperature, will it be hot?
The mean square speed of the molecules of a gas at absolute temperature T is proportional to
The temperature and pressure at Simla are 15.0°C and 72.0 cm of mercury and at Kalka these are 35.0°C and 76.0 cm of mercury. Find the ratio of air density at Kalka to the air density at Simla.
Use R=8.314J K-1 mol-1
The average translational kinetic energy of air molecules is 0.040 eV (1 eV = 1.6 × 10−19J). Calculate the temperature of the air. Boltzmann constant k = 1.38 × 10−23 J K−1.
Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.
Use R = 8.3 J K-1 mol-1
Using figure, find the boiling point of methyl alcohol at 1 atm (760 mm of mercury) and at 0.5 atm.
An adiabatic cylindrical tube of cross-sectional area 1 cm2 is closed at one end and fitted with a piston at the other end. The tube contains 0.03 g of an ideal gas. At 1 atm pressure and at the temperature of the surrounding, the length of the gas column is 40 cm. The piston is suddenly pulled out to double the length of the column. The pressure of the gas falls to 0.355 atm. Find the speed of sound in the gas at atmospheric temperature.
If a = 0.72 and r = 0.24, then the value of tr is ______.
Answer in brief:
Show that rms velocity of an oxygen molecule is `sqrt2` times that of a sulfur dioxide molecule at S.T.P.
In an ideal gas, the molecules possess ______.
Energy is emitted from a hole in an electric furnace at the rate of 20 W when the temperature of the furnace is 727°C. What is the area of the hole? (Take Stefan’s constant σ to be 5.7 × 10-8 Js-1 m-2K-4.)
Calculate the value of λmax for radiation from a body having a surface temperature of 3000 K. (b = 2.897 x 10-3 m K)
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
A molecule consists of two atoms each of mass 'm' and separated by a distance 'd'. At room temperature the average rotational kinetic energy is 'E', then its angular frequency is ______.
The average translational kinetic energy of a molecule in a gas is 'E1'. The kinetic energy of the electron (e) accelerated from rest through p.d. 'V' volt is 'E2'. The temperature at which E1 = E2 is possible, is ______.
A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC. Rank the three types of molecules in decreasing order of average K.E.
If a = 0. 72 and t = 0.04, then the value of r is ______.
