Part A. A student proposes that the temperature of a liquid could be approximate
ID: 1559337 • Letter: P
Question
Part A. A student proposes that the temperature of a liquid could be approximately measured in principle by immersing an aluminum ruler marked in microns and a quartz rod in the liquid and measuring the length of the quartz rod with the ruler after thermal equilibrium is reached. Which of the following statements is correct?
1. If the length of the aluminum ruler varies linearly with temperature, the temperature scale for this thermometer could be defined simply by measuring the length of the quartz rod at the boiling point of water.
2. All of the other statements are false.
3. The true physical length of the glass rod would be shorter at the boiling point of water than it would be at the freezing point of water.
4. The higher the temperature of the liquid, the longer the length of the quartz rod as measured by the aluminum ruler.
5. This idea could not work because the thermal coefficient of linear expansion for quartz is too small.
Part B. Which of the following statements is incorrect for an ideal gas?
1. At constant pressure and gas quantity, the volume is a linear function of the temperature as measured on the Centigrade scale.
2. It is possible for two gases at the same pressure and volume to have different temperatures.
3. For two gases at the same temperature and volume, the gas with the higher pressure has the greater quantity of gas.
4. According to the ideal gas law, the pressure of a gas can be zero only at a temperature of absolute zero.
5. For two gases at the same pressure and volume, the one at the higher temperature is comprised of a larger quantity of gas.
Part C. A police car operating its siren and a Honda car are driving on the same road. The pitch of the siren is 250 Hz but the driver of the Honda car hears the siren at a pitch of 255 Hz. One of the following statements must be false. Select it.
1. The distance between the two cars is decreasing.
2. The Honda is stopped and the police car is approaching it.
3. The Honda and police car are driving in opposite directions and the speed of the Honda is less than the speed of the police car.
4. The distance between the two cars is increasing.
5. The Honda and police car are driving in the same direction and the speed of the Honda is less than the speed of the police car.
Explanation / Answer
Part A :
(1) Since coefficient of linear thermal expansion for quartz rod is approximately 100 times less than that of aluminium, we can built a thermometer such that the temperature scale for this thermometer could be defined simply by measuring the length of the quartz rod at the boiling point of water. So (1) seems to be correct.
(3) The true physical length of the glass rod would actually should be longer at the boiling point of water than it would be at the freezing point of water. SO it is false.
(4) The higher the temperature, more is the expansion of Aluminium ruler, i.e. the spacing between the two successive reading markers would increase. Thus, it will measure a less value for its length. So it is false statement. (5) explains this point correctly.
Part B:
According to PV=nrT we can easily see that all statements except the last one are correct. So, the only false statement is (5). You should try to think these statements intuitively as well.
Part C: Since Honda driver hears a frequency more than what was emitted, it is a case of doppler redshift and is only possible when the relative distances between the two is decreasing. So, incorrect statement is (4).
Hope this helps.