366725
The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is
1 \(\dfrac{1}{7}\)
2 \(\dfrac{7}{6}\)
3 \(\dfrac{6}{7}\)
4 None of these
Explanation:
Apparent coefficient of volume expansion \(\gamma_{a p p .}=\gamma_{L}-\gamma_{s}=7 \gamma_{s}-\gamma_{s}=6 \gamma_{s}\left(\right.\) given \(\left.\gamma_{L}=7 \gamma_{s}\right)\) ratio of absolute and apparent expansion of liquid \(\dfrac{\gamma_{L}}{\gamma_{\text {app. }}}=\dfrac{7 \gamma_{s}}{6 \gamma_{s}}=\dfrac{7}{6}\)
PHXI11:THERMAL PROPERTIES OF MATTER
366726
A vessel is partly filled with a liquid. Coefficients of cubical expansion of material of vessel and liquid are \(\gamma_{V}\) and \(\gamma_{L}\) respectively. If the system is heated, then volume unoccupied by the liquid will necessarily
1 Remain unchanged if \(\gamma_{V}=\gamma_{L}\)
2 Increase if \(\gamma_{V}=\gamma_{L}\)
3 Decrease if \(\gamma_{V}=\gamma_{L}\)
4 None of the above
Explanation:
Since the vessel is partly filled, volume of the vessel is greater than that of the liquid. Hence on heating expansion of vessel will be greater than that of liquid, since \(\gamma_{V}=\gamma_{L}\). It means unoccupied volume will necessarily increase. So, option (2) is correct.
PHXI11:THERMAL PROPERTIES OF MATTER
366727
Two resistances of equal magnitude \(R\) and having temperature coefficient \(\alpha\) respectively are connected in parallel. The temperature coefficient of the parallel combination is, approximately:
366728
Two identical similar rods of metal are welded end to end as shown in figure. 20 \(cal\) of heat flows through it in 4 minutes. If the rods are welded as shown in the figure the same amount of heat will flow through the rods in
1 \(1 \mathrm{~min}\)
2 \(2 \mathrm{~min}\)
3 \(4 \mathrm{~min}\)
4 \(16 \mathrm{~min}\)
Explanation:
\(\mathrm{As}, \dfrac{Q}{t}=\dfrac{k A \Delta \theta}{l}=\dfrac{\Delta \theta}{(l / k A)}=\dfrac{\Delta \theta}{R}\) (\(R\)- Thermal resistance) Given that \(Q\) and \(\Delta \theta\) are same for two combinations. \(\begin{aligned}& t \propto R \\& \dfrac{t_{p}}{t_{s}}=\dfrac{R_{p}}{R_{s}}=\dfrac{R / 2}{2 R}=\dfrac{1}{4} \\& t_{p}=\dfrac{t_{s}}{4}=\dfrac{4}{4}=1 \mathrm{~min} .\end{aligned}\)
366725
The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is
1 \(\dfrac{1}{7}\)
2 \(\dfrac{7}{6}\)
3 \(\dfrac{6}{7}\)
4 None of these
Explanation:
Apparent coefficient of volume expansion \(\gamma_{a p p .}=\gamma_{L}-\gamma_{s}=7 \gamma_{s}-\gamma_{s}=6 \gamma_{s}\left(\right.\) given \(\left.\gamma_{L}=7 \gamma_{s}\right)\) ratio of absolute and apparent expansion of liquid \(\dfrac{\gamma_{L}}{\gamma_{\text {app. }}}=\dfrac{7 \gamma_{s}}{6 \gamma_{s}}=\dfrac{7}{6}\)
PHXI11:THERMAL PROPERTIES OF MATTER
366726
A vessel is partly filled with a liquid. Coefficients of cubical expansion of material of vessel and liquid are \(\gamma_{V}\) and \(\gamma_{L}\) respectively. If the system is heated, then volume unoccupied by the liquid will necessarily
1 Remain unchanged if \(\gamma_{V}=\gamma_{L}\)
2 Increase if \(\gamma_{V}=\gamma_{L}\)
3 Decrease if \(\gamma_{V}=\gamma_{L}\)
4 None of the above
Explanation:
Since the vessel is partly filled, volume of the vessel is greater than that of the liquid. Hence on heating expansion of vessel will be greater than that of liquid, since \(\gamma_{V}=\gamma_{L}\). It means unoccupied volume will necessarily increase. So, option (2) is correct.
PHXI11:THERMAL PROPERTIES OF MATTER
366727
Two resistances of equal magnitude \(R\) and having temperature coefficient \(\alpha\) respectively are connected in parallel. The temperature coefficient of the parallel combination is, approximately:
366728
Two identical similar rods of metal are welded end to end as shown in figure. 20 \(cal\) of heat flows through it in 4 minutes. If the rods are welded as shown in the figure the same amount of heat will flow through the rods in
1 \(1 \mathrm{~min}\)
2 \(2 \mathrm{~min}\)
3 \(4 \mathrm{~min}\)
4 \(16 \mathrm{~min}\)
Explanation:
\(\mathrm{As}, \dfrac{Q}{t}=\dfrac{k A \Delta \theta}{l}=\dfrac{\Delta \theta}{(l / k A)}=\dfrac{\Delta \theta}{R}\) (\(R\)- Thermal resistance) Given that \(Q\) and \(\Delta \theta\) are same for two combinations. \(\begin{aligned}& t \propto R \\& \dfrac{t_{p}}{t_{s}}=\dfrac{R_{p}}{R_{s}}=\dfrac{R / 2}{2 R}=\dfrac{1}{4} \\& t_{p}=\dfrac{t_{s}}{4}=\dfrac{4}{4}=1 \mathrm{~min} .\end{aligned}\)
366725
The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is
1 \(\dfrac{1}{7}\)
2 \(\dfrac{7}{6}\)
3 \(\dfrac{6}{7}\)
4 None of these
Explanation:
Apparent coefficient of volume expansion \(\gamma_{a p p .}=\gamma_{L}-\gamma_{s}=7 \gamma_{s}-\gamma_{s}=6 \gamma_{s}\left(\right.\) given \(\left.\gamma_{L}=7 \gamma_{s}\right)\) ratio of absolute and apparent expansion of liquid \(\dfrac{\gamma_{L}}{\gamma_{\text {app. }}}=\dfrac{7 \gamma_{s}}{6 \gamma_{s}}=\dfrac{7}{6}\)
PHXI11:THERMAL PROPERTIES OF MATTER
366726
A vessel is partly filled with a liquid. Coefficients of cubical expansion of material of vessel and liquid are \(\gamma_{V}\) and \(\gamma_{L}\) respectively. If the system is heated, then volume unoccupied by the liquid will necessarily
1 Remain unchanged if \(\gamma_{V}=\gamma_{L}\)
2 Increase if \(\gamma_{V}=\gamma_{L}\)
3 Decrease if \(\gamma_{V}=\gamma_{L}\)
4 None of the above
Explanation:
Since the vessel is partly filled, volume of the vessel is greater than that of the liquid. Hence on heating expansion of vessel will be greater than that of liquid, since \(\gamma_{V}=\gamma_{L}\). It means unoccupied volume will necessarily increase. So, option (2) is correct.
PHXI11:THERMAL PROPERTIES OF MATTER
366727
Two resistances of equal magnitude \(R\) and having temperature coefficient \(\alpha\) respectively are connected in parallel. The temperature coefficient of the parallel combination is, approximately:
366728
Two identical similar rods of metal are welded end to end as shown in figure. 20 \(cal\) of heat flows through it in 4 minutes. If the rods are welded as shown in the figure the same amount of heat will flow through the rods in
1 \(1 \mathrm{~min}\)
2 \(2 \mathrm{~min}\)
3 \(4 \mathrm{~min}\)
4 \(16 \mathrm{~min}\)
Explanation:
\(\mathrm{As}, \dfrac{Q}{t}=\dfrac{k A \Delta \theta}{l}=\dfrac{\Delta \theta}{(l / k A)}=\dfrac{\Delta \theta}{R}\) (\(R\)- Thermal resistance) Given that \(Q\) and \(\Delta \theta\) are same for two combinations. \(\begin{aligned}& t \propto R \\& \dfrac{t_{p}}{t_{s}}=\dfrac{R_{p}}{R_{s}}=\dfrac{R / 2}{2 R}=\dfrac{1}{4} \\& t_{p}=\dfrac{t_{s}}{4}=\dfrac{4}{4}=1 \mathrm{~min} .\end{aligned}\)
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PHXI11:THERMAL PROPERTIES OF MATTER
366725
The absolute coefficient of expansion of a liquid is 7 times that the volume coefficient of expansion of the vessel. Then the ratio of absolute and apparent expansion of the liquid is
1 \(\dfrac{1}{7}\)
2 \(\dfrac{7}{6}\)
3 \(\dfrac{6}{7}\)
4 None of these
Explanation:
Apparent coefficient of volume expansion \(\gamma_{a p p .}=\gamma_{L}-\gamma_{s}=7 \gamma_{s}-\gamma_{s}=6 \gamma_{s}\left(\right.\) given \(\left.\gamma_{L}=7 \gamma_{s}\right)\) ratio of absolute and apparent expansion of liquid \(\dfrac{\gamma_{L}}{\gamma_{\text {app. }}}=\dfrac{7 \gamma_{s}}{6 \gamma_{s}}=\dfrac{7}{6}\)
PHXI11:THERMAL PROPERTIES OF MATTER
366726
A vessel is partly filled with a liquid. Coefficients of cubical expansion of material of vessel and liquid are \(\gamma_{V}\) and \(\gamma_{L}\) respectively. If the system is heated, then volume unoccupied by the liquid will necessarily
1 Remain unchanged if \(\gamma_{V}=\gamma_{L}\)
2 Increase if \(\gamma_{V}=\gamma_{L}\)
3 Decrease if \(\gamma_{V}=\gamma_{L}\)
4 None of the above
Explanation:
Since the vessel is partly filled, volume of the vessel is greater than that of the liquid. Hence on heating expansion of vessel will be greater than that of liquid, since \(\gamma_{V}=\gamma_{L}\). It means unoccupied volume will necessarily increase. So, option (2) is correct.
PHXI11:THERMAL PROPERTIES OF MATTER
366727
Two resistances of equal magnitude \(R\) and having temperature coefficient \(\alpha\) respectively are connected in parallel. The temperature coefficient of the parallel combination is, approximately:
366728
Two identical similar rods of metal are welded end to end as shown in figure. 20 \(cal\) of heat flows through it in 4 minutes. If the rods are welded as shown in the figure the same amount of heat will flow through the rods in
1 \(1 \mathrm{~min}\)
2 \(2 \mathrm{~min}\)
3 \(4 \mathrm{~min}\)
4 \(16 \mathrm{~min}\)
Explanation:
\(\mathrm{As}, \dfrac{Q}{t}=\dfrac{k A \Delta \theta}{l}=\dfrac{\Delta \theta}{(l / k A)}=\dfrac{\Delta \theta}{R}\) (\(R\)- Thermal resistance) Given that \(Q\) and \(\Delta \theta\) are same for two combinations. \(\begin{aligned}& t \propto R \\& \dfrac{t_{p}}{t_{s}}=\dfrac{R_{p}}{R_{s}}=\dfrac{R / 2}{2 R}=\dfrac{1}{4} \\& t_{p}=\dfrac{t_{s}}{4}=\dfrac{4}{4}=1 \mathrm{~min} .\end{aligned}\)
