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
When we place a gas cylinder on a van and the van moves, does the kinetic energy of the molecules increase? Does the temperature increase?
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?
The process on an ideal gas, shown in figure, is
Find the number of molecules of an ideal gas in a volume of 1.000 cm3 at STP.
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
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.
Answer in brief:
A gas in a cylinder is at pressure P. If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then find the resultant pressure.
Calculate the ratio of the mean square speeds of molecules of a gas at 30 K and 120 K.
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.)
Compare the rates of emission of heat by a blackbody maintained at 727°C and at 227°C, if the black bodies are surrounded by an enclosure (black) at 27°C. What would be the ratio of their rates of loss of heat?
The number of degrees of freedom, for the vibrational motion of a polyatomic molecule, depends on the ______
Why the temperature of all bodies remains constant at room temperature?
What is the microscopic origin of temperature?
The average K.E. of hydrogen molecules at 27° C is E. The average K.E. at 627° C is ____________.
A ring of mass m and radius r rotates about an axis passing through its centre and perpendicular to its plane with angular velocity `omega`. Its kinetic energy is ______.
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 ______.
A cylinder containing an ideal gas is in vertical position and has a piston of mass M that is able to move up or down without friction (Figure). If the temperature is increased ______.
Two molecules of a gas have speeds of 9 × 10 6 ms−1 and 1 × 106 ms−1, respectively. What is the root mean square speed of these molecules?
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.
